Sally has 30 coins in her pocket, some of which are nickels, the rest of which are dimes.If the coins have a value of $2.40, how many of each kind does she have?
Please tell me how do did it and show your work.Thanks a million!
2006-12-17 12:26:31 · 5 answers · asked by Jordan 2 in Science & Mathematics ➔ Mathematics
I thought I was stumped with this question but I figured it out. Thanks for all who answered it!
2006-12-17 12:42:04 · update #1
If she had $2.40 only in dimes, she would have 24 coins. Trade one dime for 2 nickels, and you have one extra coin. With 24 coins, you are 6 short of the 30 needed, so you need to trade 6 dimes for a pair of nickels each. So, you have 24-6 = 18 dimes for $1.80, and 12 nickels (for $0.60). Total $2.40 and 30 coins.
2006-12-17 12:30:58 · answer #1 · answered by Vincent G 7 · 1⤊ 0⤋
Vincent is correct.
ANother way to do this is using linear algebra:
let n be the number of dimes, m the number of nickels
n+m = 30
10n+5m = 240
Multiply the first equation by 10:
10n+10m = 300
subtract equation 2:
10n+5m = 240
5m = 60
m = 12
So there are 12 nickels, and since n+m = 30, 18 dimes.
2006-12-17 20:33:01 · answer #2 · answered by firefly 6 · 0⤊ 0⤋
Let:
x = number of nickels
y = number of dimes
Then we have:
Number of Coins
x + y = 30
x = 30 - y
Amount of Money
5x + 10y = 240
x + 2y = 48
(30 - y) + 2y = 48
30 + y = 48
y = 18
x = 30 - y = 30 - 18 = 12
So there are 12 nickels and 18 dimes.
2006-12-17 20:40:11 · answer #3 · answered by Northstar 7 · 0⤊ 0⤋
n+d=30
5n+10d=240 divide by 5
n+2d=48
n+d=30 subtract
d=18
n+18=30
n=12
check 5*12+10*18=60+180=240
12 nickels & 18 dimes
2006-12-17 21:19:59 · answer #4 · answered by yupchagee 7 · 0⤊ 0⤋
18 dimes and 12 nickles
2006-12-17 20:34:02 · answer #5 · answered by Jack B. Nimble 2 · 0⤊ 0⤋